The criterion of the distance relay based on the power-frequency voltage and current variation is analyzed in detail and will get the criterion of various faults when the relay passes through transition resistance. There is difference between the single-phase-to-ground fault and the phase-phase direct short-circuit fault. The criterion of three-phase symmetrical fault and phase-phase-ground fault of various types are similar as phase-phase short-circuit fault. And it points out:transition resistance has the most important influence on relay performance when the single-phase grounding fault occurred, and second to phase-to-phase short-circuit fault. The threshold resistance is defined as the maximum tolerance transition resistance which the relay could correct operated, and the calculation formula of the threshold resistance is derived. The definition of sequence-current-distribution coefficient, adjusting-factor, threshold resistance curve are given, which points out:sequence-current-distribution coefficient will be accompanied by system-operating-status changed, fault distance changed, and the threshold resistance changed. The load and amplitude-ratio of the two ends have great influence on the adjusting factor. Reducing the adjusting factor makes for increasing the threshold resistance and the protection scope of the relay. The correctness of the above analysis is verified by Matlab simulation.